The BBC used undercover reporters to investigate working conditions at Pegatron factories in Shanghai,China, where it claimed workers completed shifts of up to 16 hours.
The BBC report alleged that workers fell asleep during 12 hour shifts on the iPhone 6 production line and were made to work 18 days in a row after repeatedly being denied requests for a day off.
Williams countered that Apple has tracked the weekly hours of over one million workers within its supply chain, and that its suppliers have achieved an average of 93 per cent compliance with the 60-hour workweek limit this year.
" We know of no other company doing as much as Apple does to ensure fair and safe working conditions, to discover and investigate problems, to fix and follow through when issues arise, and to provide transparency into the operations of our suppliers," he said.
Panorama also claimed to find children working in dangerous conditions on the Indonesian island of Bangka.
"Apple has publicly stated that tin from Indonesia ends up in our products, and some of that tin likely comes from illegal mines," Williams countered.
"Tens of thousands of artisanal miners are selling tin through many middlemen to the smelters who supply to component suppliers who sell to the world. The government is not addressing the issue, and there is widespread corruption in the undeveloped supply chain. Our team visited the same parts of Indonesia visited by the BBC, and of course we are appalled by what’s going on there.
Apple has created an Indonesian Tin Working Group with other technology companies, and is seeking to implement a system to hold tin smelters accountable, he added.
"We know there are a lot of issues out there, and our work is never done. We will not rest until every person in our supply chain is treated with the respect and dignity they deserve," he concluded.
Pegatron said they were carefully investigating the BBC's claims, and will take "all necessary actions".
Apple's letter to UK staff in full was published online by Telegraph.co.uk here.